Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a “classical” account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed system of random variables, one variable for every value of every input (in psychology) or every measurement on every particle involved (in an EPR experiment). We overview three classes of necessary conditions (some of them also sufficient under additional constraints) for the existence of such joint distributions.
KeywordsBell-CHSH-Fine inequalities cosphericity test EPR paradigm joint distribution criterion linear feasibility test non-commuting measurements pseudo-quasi-metrics on random variables quantum entanglement selective influences
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